{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spectral derivative in NumPy\n",
    "\n",
    "$$ f'(x) = \\text{ifft}(i k \\; \\text{fft}(f(x))) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 1\n",
    "N = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# IMPORTANT: The right boundary point is not included in the mesh!\n",
    "mesh = np.linspace(0, L, N, endpoint=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: np.sin(4 * np.pi * x)\n",
    "f_prime = lambda x: 4 * np.pi * np.cos(4 * np.pi * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_h = f(mesh)\n",
    "f_prime_h = f_prime(mesh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f198a37a080>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mesh, f_h, label=\"original\")\n",
    "plt.plot(mesh, f_prime_h, label=\"analytical derivative\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = np.fft.fftfreq(N, d=L/(N * 2 * np.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_prime_fft_h = np.fft.ifft(1j * k * np.fft.fft(f_h)).real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f19899686d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mesh, f_h, label=\"original\")\n",
    "plt.plot(mesh, f_prime_h, label=\"analytical derivative\")\n",
    "plt.plot(mesh, f_prime_fft_h, label=\"spectral derivative\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "265371ff1b98b9f4eaa16d44fb1eb5bb5e02f4557e1c68186d1d500959ccd159"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
